Question: Solve for $x$ and $y$ using elimination. ${-3x+4y = 9}$ ${-5x+5y = 5}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-5$ and the bottom equation by $4$ ${15x-20y = -45}$ $-20x+20y = 20$ Add the top and bottom equations together. $-5x = -25$ $\dfrac{-5x}{{-5}} = \dfrac{-25}{{-5}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-3x+4y = 9}\thinspace$ to find $y$ ${-3}{(5)}{ + 4y = 9}$ $-15+4y = 9$ $-15{+15} + 4y = 9{+15}$ $4y = 24$ $\dfrac{4y}{{4}} = \dfrac{24}{{4}}$ ${y = 6}$ You can also plug ${x = 5}$ into $\thinspace {-5x+5y = 5}\thinspace$ and get the same answer for $y$ : ${-5}{(5)}{ + 5y = 5}$ ${y = 6}$